It is known that roughly 2/3 of all human beings have a dominant right foot or eye. Is there also right-sided dominance in kissing behavior? An article reported that in a random sample of 115 kissing couples, both people in 74 of the couples tended to lean more to the right than to the left. (Use a = 0.05.) USE SALT (a) If 2/3 of all kissing couples exhibit this right-leaning behavior, what is the probability that the number in a sample of 115 who do so differs from the expected value by at least as much as what was actually observed? (Round your answer to four decimal places.) 76.6667 Probabilities should be between 0 and 1. (b) Does the result of the experiment suggest that the 2/3 figure is implausible for kissing behavior? State the appropriate null and alternative hypotheses. O Ho: P = 2/3 Ha: p ≤ 2/3 O Ho: P = 2/3 H₂:p> 2/3 O Ho: P = 2/3 H₂: P <2/3 Ho: p= 2/3 H₂: P = 2/3 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) -0.53 z = P-value = 0.5961 State the conclusion in the problem context. O Do not reject the null hypothesis. There is sufficient evidence to conclude that the true proportion of right-leaning behavior differs from 2/3. Do not reject the null hypothesis. There is not sufficient evidence to conclude that the true proportion of right-leaning behavior differs from 2/3. O Reject the null hypothesis. There is not sufficient evidence to conclude that the true proportion of right-leaning behavior differs from 2/3. O Reject the null hypothesis. There is sufficient evidence to conclude that the true proportion of right-leaning behavior differs from 2/3.
It is known that roughly 2/3 of all human beings have a dominant right foot or eye. Is there also right-sided dominance in kissing behavior? An article reported that in a random sample of 115 kissing couples, both people in 74 of the couples tended to lean more to the right than to the left. (Use a = 0.05.) USE SALT (a) If 2/3 of all kissing couples exhibit this right-leaning behavior, what is the probability that the number in a sample of 115 who do so differs from the expected value by at least as much as what was actually observed? (Round your answer to four decimal places.) 76.6667 Probabilities should be between 0 and 1. (b) Does the result of the experiment suggest that the 2/3 figure is implausible for kissing behavior? State the appropriate null and alternative hypotheses. O Ho: P = 2/3 Ha: p ≤ 2/3 O Ho: P = 2/3 H₂:p> 2/3 O Ho: P = 2/3 H₂: P <2/3 Ho: p= 2/3 H₂: P = 2/3 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) -0.53 z = P-value = 0.5961 State the conclusion in the problem context. O Do not reject the null hypothesis. There is sufficient evidence to conclude that the true proportion of right-leaning behavior differs from 2/3. Do not reject the null hypothesis. There is not sufficient evidence to conclude that the true proportion of right-leaning behavior differs from 2/3. O Reject the null hypothesis. There is not sufficient evidence to conclude that the true proportion of right-leaning behavior differs from 2/3. O Reject the null hypothesis. There is sufficient evidence to conclude that the true proportion of right-leaning behavior differs from 2/3.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:**Is There Right-Sided Dominance in Kissing Behavior?**
It is known that roughly 2/3 of all human beings have a dominant right foot or eye. Is there also right-sided dominance in kissing behavior? An article reported that in a random sample of 115 kissing couples, both people in 74 of the couples tended to lean more to the right than to the left. (Use α = 0.05.)
### (a) Probability Calculation
If 2/3 of all kissing couples exhibit this right-leaning behavior, what is the probability that the number in a sample of 115 who do so differs from the expected value by at least as much as what was actually observed?
- **Incorrect Calculated Probability**: 76.6667
- **Note**: Probabilities should be between 0 and 1.
### (b) Hypothesis Test
Does the result of the experiment suggest that the 2/3 figure is implausible for kissing behavior? State the appropriate null and alternative hypotheses.
1. \( H_0: p = \frac{2}{3} \)
- \( H_a: p \leq \frac{2}{3} \)
2. \( H_0: p = \frac{2}{3} \)
- \( H_a: p > \frac{2}{3} \)
3. \( H_0: p = \frac{2}{3} \)
- \( H_a: p < \frac{2}{3} \)
4. **Selected**: \( H_0: p = \frac{2}{3} \)
- \( H_a: p \neq \frac{2}{3} \) ✔️
### Test Statistic Calculation
Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.)
- **Test Statistic (z)**: -0.53 ✔️
- **P-value**: 0.5961 ✔️
### Conclusion
State the conclusion in the problem context.
- Do not reject the null hypothesis. There is sufficient evidence to conclude that the true proportion of right-leaning behavior differs from 2/3.
- **Selected**: Do not reject the null hypothesis. There is not sufficient evidence to conclude that the true proportion of right-leaning behavior differs from 2
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